Computation of Hydrodynamic Characteristics of Ships using CFD

Authored by Md. Mashud Karim and Nabila Naz

2016 4th Asia Conference on Mechanical and Materials Engineering

Presented by:Md. Mashud KarimProfessorDepartment of Naval Architecture and Marine EngineeringBangladesh University of Engineering and TechnologyDhaka-1000, Bangladesh

Objective

To analyze the governing equation of fluid flow around ship hull

To determine the flow around different ship hulls with free surface

To determine the free- surface wave pattern and wave elevation around ship hulls at different speeds

To compute wave making, viscous and total resistance components at different speeds

To analyze the computed results for different mesh density

To validate the obtained results with available experimental results

The objective of present research are:

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Waves caused by the movement of ShipWhen ship moves through water creates pressure difference around it causes generation of waves at free surface to maintain constant atmospheric pressure.

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Lord Kelvin (1887) gave a characteristics wave for ship named as Kelvin wave pattern which consists of two types of waves:

Transverse wave Divergent Wave

Ship Wave Pattern

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Determination of Wave Characteristics

Real Wave Pattern

Wave Pattern simulated by CFD

Wave Pattern by EFD at Towing Tank

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What is CFD?• Stands for Computational Fluid Dynamics•virtual towing tank • determines the flow characteristics around ship by mathematical modeling and numerical methods using commercially developed software •possible by the advent of digital computer and advancing with improvements of computer resources

Substantial reduction of lead times and costs of new designs. Ability to study systems where controlled experiments are difficult or impossible to perform (e.g. very large systems). Ability to study systems under hazardous conditions at and beyond their normal performance limits (e.g. safety studies and accident scenarios). Practically unlimited level of detail of results.

Advantages of CFD over EFD

CFD software- SHIPFLOWdeveloped by FLOWTECH International AB from the long term research done at the Hydrodynamics group of the Naval Architecture Department at Chalmers University of Technology, Gothenburg, Sweden.

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To compute the flow around a ship in an efficient way, zonal approach will be is used by Shipflow as shown in Fig. which divides the flow around a ship into three different zones with different solution methods.

Fig . Zonal approach

Zone 1: Region outside the boundary layer; the potential flow theory will be employed

Zone 2: Thin boundary layer region near the forward part of the hull; ‘momentum boundary integral equation’ will be used.

Zone 3: Stern/wake region where ‘Navier Stokes equation’ will be used

Governing Equation for Zonal Approach

Zone 1 Potential flow region Fluid is incompressible and inviscid and the flow is irrotational

Continuity equation becomes

Water surface condition

Ship hull surface condition

Kinematic free-surface condition

Dynamic free-surface condition

Zone 2 Thin boundary layer region near the hull

Momentum integral equation

Zone 3 Viscous flow at stern/ wake region

Reynolds Averaged Navier Stokes (RANS) equations coupled with the time-averaged continuity equation:

Description of Hull

Body plan 3D view of hull

A mathematical hull with its geometric surface defined as: Wigley Hull

LBP 1 mB/L 0.01H/L 0.0631

WPA coefficient 0.667CB 0.447

Model Dimensions:

Body plan 3D view

Series 60 ship

LBP 1 mB/L 0.134H/L 0.05352

WPA coefficient 0.943CB 0.6

Discrtetization of hull and free-surface for potential flow

The surface of the ship and the water surface are divided into flat, ideally square panels commonly with constant source strength.

(a) Wigley Hull (b) Series 60 ship

Boundary Conditions

Boundary types employed are no slip, slip, inflow, and outflow. Both Dirichlet and Neumann boundary conditions are formulated in terms of pressure , velocity , turbulent kinetic energy , and turbulent frequency .

Due to symmetry on the x-z plane, quarter of cylinder is used as computational domain with radius 3.0 L, downstream length 0.8L

For zonal approach viscous computation starts from 0.5L behind the F.P of the ship as shown in Fig.Fig. Computational Domain

Grid Generation

Fig. H-O type structured grid(a) computational domain (b) close-up view

Computational domain along with hull geometry is represented by a single block structured grid of H-O type with 0.45 M cells as shown in Fig.

(b) Fr. 0.408

Wave Pattern around Wigley hull at Different Speed

(a) Fr. 0.177

Wave pattern consists of two wave systems namely transverse and divergent waves

Divergent waves which are the primary wave system at lower Fr., start at the bow and stern region at an angle of 19.47º

Wave Pattern around Series 60 Ship at Different Speed

(a) Fr. 0.20 (b) Fr. 0.35

Transverse waves which are more important at higher Fr. are perpendicular to the ship's line of motion.

Both wave patterns are contained within two straight lines making an angle of 19.47º on each side of line of motion show the characteristics of Kelvin wave pattern

Free Surface Wave Elevation

Wigley hull at Fr. 0.267

The computed free-surface wave elevations around Wigley hull with different mesh configuration at Fr. 0.267 are compared with the experimental results as shown in Fig.

It appears that with fine mesh wave elevation along hull shows good agreement with the experimental results except the stern region for Wigley hull

Free Surface Wave Elevation

Series 60 ship at Fr. 0.316

The computed free-surface wave elevations around Series 60 ship with different mesh configuration at Fr. 0.316 are compared with the experimental results as shown in Fig.

It appears that with fine mesh wave elevation along hull shows good agreement with the experimental results except the bow region for Series 60

This discrepancy between computed and experimental results is likely to have been caused by the following reasons:

(i)the wave profiles are taken from the free- surface elevations at the panels next to the body, not at the actual hull surface, which resulted in error especially near the bow and stern region.

(ii) Potential flow methods assumes free surface as flat and rigid to avoid air/water interface of viscous flow which also results in variation between computed and experimental results.

Pressure Coefficient and Potential Flow Streamline

(a) Wigley hull (b) Series 60 ship

Pressure coefficient and potential flow streamlines are automatically traced from the potential flow solution.

Boundary layer tracing is started from 0.05L behind the fore perpendicular to the beginning of the after hull part as shown in Figs. at Fr. 25 for both hulls.

Resistance coefficient as a function of Fr.Total (Ct), wave making (Cw) and viscous (Cv) resistance coefficients as a function of Froude numbers (Fr) and Reynolds numbers (Re) are shown in Fig.

Cv decreases with increasing Re for both hulls as it largely depends on it. Curves of Cw and Ct consist of number of humps and hollows which occur when bow and stern waves are in and out of phase respectively which is validated with experimental results.

(a) Wigley hull (b) Series 60 ship

WIGLEY HULL: RELATIVE ERRORS OF TOTAL RESISTANCE COEFFICIENTS BETWEEN CFD

AND EFD

Fr. Re. Ct CFD Ct EFD Error (%)

0.177 2.2*106 0.00433 0.00419 -3.34129

0.25 3.1*106 0.00479 0.00455 -5.27473

0.27 3.3*106 0.00475 0.00447 -6.26398

0.316 3.9*106 0.00544 0.00516 -5.42636

0.35 4.3*106 0.00517 0.00489 -5.72597

0.408 5.0*106 0.00624 0.00573 -8.90052

From Table I it is seen that for Wigley hull CFD results of Ct is greater than the EFD results for all Fr. and maximum relative error is 8.9% at the highest Fr. of the range.

Table I

SERIES 60 SHIP: RELATIVE ERRORS OF TOTAL RESISTANCE COEFFICIENTS BETWEEN CFD

AND EFD

Fr. Re. Ct CFD Ct EFD Error (%)

0.1 1.2*106 0.00474 0.00476 0.42017

0.15 1.7*106 0.00448 0.00456 1.75439

0.2 2.2*106 0.00455 0.00442 -2.94118

0.25 3.1*106 0.00457 0.00448 -2.00893

0.3 3.8*106 0.00619 0.00594 -4.20875

0.35 4.3*106 0.00653 0.00645 -1.24031

Table II

Table II shows that for Series 60 ship at low Fr. CFD results of Ct is smaller than the EFD results but as Fr. increases, CFD starts to overestimate the Ct than EFD with maximum relative error of 4.21% at Fr. 0.3.

ConclusionsIn this research work, potential flow, boundary layer flow and viscous flow theories are used to determine flow characteristics at different regions. From the above mentioned results and discussions, following conclusions can be drawn:

I. Zonal approach for computing flow characteristics takes less computational time than global approach as three solvers act successively to give results significant to that region

ii. Wave pattern around ship hulls with different Fr. show characteristics of Kelvin wave pattern and computed wave elevations agree satisfactorily with experimental results

iii. With increasing Fr. wave making and total resistance is accompanied by a number of humps and hollows due to interaction of divergent waves and frictional resistance decreases as Re. increases for both hulls

iv. The computed results depend to a certain extent on the discretization of the body and the free-surface. The agreement between the computed and experimental results is quite satisfactory with increasing number of panels. However, it takes longer computation time.

ACKNOWLEDGMENT

Authors are grateful to Bangladesh University of Engineering and Technology (BUET) and sub-project CP # 2084 of Department of Naval Architecture and Marine Engineering under Higher Education Quality Enhancement Project (HEQEP), UGC, Ministry of Education, Govt. of Bangladesh for providing necessary research facilities during the current research work.